Transcript 1 7 Formulas 02

1.7: Various Formulas, Part 2
Objectives:
1. To identify various
polyhedra and solids
of revolution
2. To use formulas to
find the volume of
prisms, pyramids,
cylinders, cones, and
spheres
Assignment:
• 1.7 Various Formulas
Worksheet: 21-35
Objective 1
You will be able to identify various
polyhedra and solids of revolution
In Glorious 3-D!
Most of the figures you have worked with so
far have been confined to a plane—twodimensional. Solid figures in the “real
world” have 3 dimensions: length, width,
and height.
Polyhedron
A solid formed by polygons that enclose a
single region of space is called a
polyhedron.
Parts of Polyhedrons
• Polygonal region = face
• Intersection of 2 faces = edge
• Intersection of 3+ edges = vertex
face
edge
vertex
Exercise 10
a. Name all of the
faces
b. Name all of the
edges
c. Name all of the
vertices
Classifying Polyhedra
Polyhedrons are classified by the # of faces:
[Insert Greek prefix for # of faces]-hedron
Regular Polyhedron
A regular
polyhedron is
a polyhedron
whose faces
are regular
congruent
polygons.
Regular Polyhedron
Regular
polyhedra
are
commonly
called
Platonic
solids.
Classification of Prisms
Prisms are classified by their bases.
Classification of Pyramids
Pyramids are also classified by their bases.
Exercise 11
Solids of Revolution
Cylinder
Cone
Objective 2
You will be able to use
formulas to find the volume
of prisms, pyramids,
cylinders, cones, and
spheres
Volume
Volume is the measure
of the amount of space
contained in a solid,
measured in cubic
units.
This is simply the number of
unit cubes that can be
arranged to completely fill the
space within a figure.
Exercise 12
Find the volume of
the given figure in
cubic units.
More Formulas!
The volume of a solid is also easily
computed with a formula.
What does the B represent?
Exercise 13
The previous formulas for volume all
contained B, the area of the base. Rewrite
the following formulas without B.
1. Rectangular Prism:
2. Cylinder:
3. Cone:
Exercise 14
Find the volume
of each solid.
Exercise 15
The triangle shown
can be rotated
around the y-axis or
the x-axis to make
two different solids
of revolution.
Which solid would
have the greater
volume?
Exercise 16
A pipe in the shape of a
cylinder with a 30-inch
diameter is to go through
a passageway shaped
like a rectangular prism.
The passageway is 3 ft
high, 4 ft wide, and 6 ft
long. The space around
the pipe is to be filled with
insulating material.
Exercise 16
What is the volume of the
insulating material?
1.7: Various Formulas, Part 2
Objectives:
1. To identify various
polyhedra and solids
of revolution
2. To use formulas to
find the volume of
prisms, pyramids,
cylinders, cones, and
spheres
Assignment:
• 1.7 Various Formulas
Worksheet: 21-35